Flywheel systems have been known in the art for a number of years, and have proven to be extremely useful in industrial settings (as, for example, uninterruptible power supplies) due to their excellent ability to generate, store and recover kinetic energy. A typical flywheel includes a flywheel, a shaft to which the flywheel is secured, as well as one or more bearing assemblies that rotatably support the shaft. A flywheel system also includes a protective outer rim, which is supported by a hub that serves to connect the rim to the shaft.
In operation, a high-powered, high-strength motor drives the shaft, which itself drives a rotor at a high velocity. This causes the rim of the flywheel system to rotate/spin rapidly, which, in turn, creates a significant amount of kinetic energy in accordance with the following equation:Energy=½*(rim density)*(rim volume)*(rotor radius of gyration)2*(rotational speed of rim)2
Since the advent of flywheels, those in this art have constantly aimed to design a flywheel system that is able to generate as much kinetic energy as possible according to this equation without compromising the safe operation of the flywheel system. To that end, several years ago, designers began to experiment with switching from metal-based to composite-based rims.
Metal-based rims had proven problematic in use because their somewhat low yield strength limited their ability to generate rotational speed and, therefore, the ability of the flywheel system to generate significant amounts of kinetic energy. And although metal-based rims had proven highly failure resistant, when they did fail, they tended to break into three large, heavy pieces, which were jettisoned from the flywheel system, thus presenting a danger to surrounding persons and property alike.
Composite-based rims are not only lighter than metal-based rims, but can have comparable or even higher strengths and stiffnesses, thus allowing them to achieve much higher rotational speeds and, therefore, to apparently provide most, if not all of the benefits of metal-based rims, without the aforementioned risks/drawbacks.
Not surprisingly, within just a few years of their discovery, composite based rims had become the standard in the flywheel system industry.
More recently, however, it has become evident that composite-based rims also encounter problems in use, chief among which is their susceptibility to failure due to radial stresses and strains that arise during operation of a flywheel system.
As noted above, flywheel systems that incorporate composite-based rims are primarily advantageous as compared to metal-based rims because their lower weight allows them to be able to rotate more rapidly than metal-based rims and, in turn, to generate more energy for storage than would be generated by an otherwise identically dimensioned metal-based rim. But as the speed of rotation of any flywheel system rim (whether metal- or composite-based) increases, so too does the undesirable strain, and hoop/radial stresses placed against it according to the equations:Hoop Stress=(rim density)*(rim radius)2*(rim rotational speed)2=(strain)*(modulus) Radial Stress˜(rim density)*(rim Thickness)2*(rim rotational speed)2
Thus, for example, according to the second equation, a first rotating rim that is twice as thick as a second rotating rim will accumulate approximately four times more radial stresses than the second rotating rim. This marked increase in the generation of stresses and strains in a composite-based rim, which has a relatively low radial strength as compared to its hoop strength.
Realizing this, but not wanting to sacrifice the benefit(s) of increased rim rotational speed (and, thus, increased kinetic energy), some suggested reducing the overall thickness of composite-based rims, while increasing the rims' overall length.
The likely rationale for doing so was the fact that the square of the rim thickness is proportional to the amount of strain and radial stress encountered in the rim, such that a decreased rim thickness should offset enough of the increase in rotational speed of the rim to keep the amount of strain and radial stress encountered in the rim within a manageable range. The reason that the length of the rim (which, when factored into the rim volume, is proportional to the amount of kinetic energy produced by the rim) was increased was to compensate for the reduction in energy that would be caused by reducing the rim's cross sectional area, the square of which is also directly proportional to the amount of kinetic energy generated by the rim.
Unfortunately, flywheel systems that incorporated rims with both reduced thickness and increased lengths proved to be unduly expensive not only to produce but also to implement and operate in usage environments, and, therefore, quickly grew out of favor in the art.
Therefore, a need remains for a composite-based rim for use in flywheel systems, wherein the design of the rim positively influences the ability of the rim to generate energy without negatively influencing, due to the generation of unmanageable radial stresses and strains, the rim's longevity and the safe operation of a flywheel system within which the rim is incorporated.